If n(A ∪ B ∪ C) = 118, n(A) = 45, n(B) = 50, n(C) = 55, n(A ∩ B) = 18, n(B ∩ C) = 20, and n(C ∩ A) = 16, what is n(A ∩ B ∩ C)?
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Answer and explanation
Correct answer: 22
Use the three-set inclusion–exclusion formula. Let x = n(A ∩ B ∩ C). Then 118 = 45 + 50 + 55 − 18 − 20 − 16 + x. The known terms give 150 − 54 = 96, so 118 = 96 + x and x = 22. Therefore, the triple intersection contains 22 elements, making option A correct.
Frequently asked questions
What is the correct answer to this question?
22
Why is this the correct answer?
Use the three-set inclusion–exclusion formula. Let x = n(A ∩ B ∩ C). Then 118 = 45 + 50 + 55 − 18 − 20 − 16 + x. The known terms give 150 − 54 = 96, so 118 = 96 + x and x = 22. Therefore, the triple intersection contains 22 elements, making option A correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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